Anyway, I think I was thinking that including the difference from the average value would help the neural network identify pairs. In retrospect, it should have been able to recognize that simply from the card values, no?

Limit holdem had been done a lot and No Limit was my area of expertise, which is why I chose it. I didn't have that much experience with shortstacking, but I had read pretty much everything there was to read on it and it seemed like a good start because of its simplicity. Little did I know that the profits from shortstacking come from a very few carefully timed moves that are close to impossible for a rules-based bot to emulate (more on that in another post). Eventually I decided to build a no limit heads up bot, which is where my success wound up being.

I didn't mention it in the post, but the key was moving away from rules based to a value based system, where the bot calculated the profitability of its options and decided based on that. It was a lot easier to debug, but there were a whole set of challenges to that too, like estimating your opponent's range.

Instantiating the features correctly is crucial to getting good neural network accuracy.

It might be the case that a thermometer representation for the card value is more appropriate. The thermometer representation is that there are thirteen bit-values, and the first n values are on for the value n.

Using this sort of input representation, the network can model the non-linear relationship between different card values, instead of assuming a strictly linear correlation.